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Alexander A. BalandinNano-Device LaboratoryDepartment of Electrical Engineering andMaterials Science and Engineering ProgramUniversity of California – Riverside
Bremen, Germany – Keynote Talk – 2013
Phononics in Low-Dimensional Materials: Engineering Phonon Spectrum
Alexander A. Balandin, University of California - Riverside
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UCR Bell Tower
City of Riverside
UCR Botanic Gardens
Joshua Tree Park, California
UCR Engineering Building
Alexander A. Balandin, University of California - Riverside
Nano-Device Laboratory (NDL) Department of Electrical EngineeringUniversity of California – Riverside
Profile: experimental and theoretical research in advanced materials and nano-devices
Phononics Research & Applications
Raman, Fluorescence and PL Spectroscopy
Electronic Devices and
Circuits
Optoelectronics
Direct Energy Conversion
Bio-Nanotech
Thermal and Electrical Characterization
Device Design and Characterization
Nanoscale Characterization
Theory and Modeling
PI: Alexander A. Balandin
Alexander A. Balandin, University of California - Riverside
Outline
Part I: Overview of Phononics and Phonon Engineering
Part II: Phonons in Graphene Specifics of 2D phonon thermal transport
Engineering phonons by twisting atomic planes
Part III: Phonons in van der Waals Materials Restacking the layers
Charge-density waves
Part IV: Applications of Phononics Thermal interface materials
Heat spreaders
Thermoelectric energy generation
Low-power information processing
Conclusions 4
Alexander A. Balandin, University of California - Riverside
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Part I: Overview of Phononics and Phonon Engineering
Cross sections of polar optical phonon modes with l = 3, 4 and for the spherical ZnO quantum dot. Blue and red colors denote negative and positive values of phonon potentials, correspondingly.
Alexander A. Balandin, University of California - Riverside6
Phononics Nanoscale Phonon Engineering
Definition: phonon engineering is an approach for modifying the thermal, electrical and optical properties of materials via tuning the phonon characteristics at nanometer scale through the spatial confinement-induced changes in the phonon spectrum.
EG
Band-structure engineering: mismatch of EG
Phonon engineering: mismatch of Z=rVsound
Z2
Z1
Acoustic Impedance:Z=rVs [kg/m2s]
Tuning Parameters:
Crystalline structure
Dimensions
Sound velocity
Mass density
Acoustic Impedance
Interface
Optical phonon
frequencies
Goals:
Change in electron –phonon scattering drift mobility
Change in phonon group velocity thermal conductivity
Control of the phonon energies optical response A.A. Balandin, "Nanophononics: Phonon engineering in
nanostructures and nanodevices," J. Nanoscience and Nanotechnology, 5, 7 (2005).
Alexander A. Balandin, University of California - Riverside
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Rytov Model for Folded Phonons in Thinly Laminated Media
wave vector q (1/nm)
w (rad/s)
p/ap/D
w=Vq
q
,sinsin2
1coscos)cos(
2
2
1
12
2
2
1
1
V
D
V
D
V
D
V
DqD
wwww
Vi is the sound velocity in each layer, and z=r2V2/r1V1 is the acoustic mismatch between the layers, D=D1+D2 is the period of the superlattice.
Rytov (1956) Model for Thinly Laminated Medium
Raman spectrum of superlattice. Inset is Rytov-model calculations showing q of the folded LA peaks. The arrows indicate predicted peak frequencies corresponding to a superlattice period of 52 A.
The data is after C. Colvard et al., Phys. Rev. B, 31, 2080 (1985)
S. M. Rytov, Soviet Physics - Acoustics, 2, 67 (1956).
Alexander A. Balandin, University of California - Riverside8
Bulk vs. Confined Acoustic Phonons
Bulk Semiconductor
E.P. Pokatilov, D.L. Nika and A.A. Balandin, “Acoustic-phonon propagation in semiconductor nanowires with elastically dissimilar barriers,” Physical Review B, 72, 113311 (2005)
D.L. Nika, E.P. Pokatilov and A.A. Balandin, "Phonon - engineered mobility enhancement in the acoustically mismatched transistor channels," Appl. Phys. Lett., 93, 173111 (2008).
Alexander A. Balandin, University of California - Riverside9
Thermal Conductivity of Nanostructures Beyond “Classical” Size Effects
“Classical” size effects on heat conduction: phonon – boundary scattering
Casimir (1938), Berman (1955), Ziman (1960) Lp
p
B
z
1
11Phonon – boundary scattering rate:
Tuning thermal conductivity
Alexander A. Balandin, University of California - Riverside10
Thermal Conductivity of Nanowires: Boundary Size Effects
Predicted decrease of the thermal conductivity from 148 W/m-K in bulk to about 13 W/m-K in 20 nm Si crystalline nanowire at T=300 K (2001).
Agreement with experimental study: ~ 9 W/m-K in 22 nm nanowire at T=300K; strong diameter dependence; deviation from Debye T3 law at low T, Majumdar Group, UCB (2003).
J. Zou and A. Balandin, Phonon heat conduction in a semiconductor nanowire, J. Applied Physics, 89, 2932 (2001.)
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Thermal Conductivity Inhibition in Phonon Engineered Nanowires
Models: Five-parameter Born-von Karman Six-parameter valence-force field K of Si/Ge cross-section
modulated nanowires is three orders of magnitude lower than that of bulk Si.
Thermal flux in the modulated nanowires is suppressed by an order of magnitude in comparison with generic Si nanowires.
Modification of phonon spectra in modulated nanowires leading to decrease of the phonon group velocities and localization of the certain phonon modes.
K inhibition is achieved in nanowires withoutadditional surface roughness.
Details: D.L. Nika, A.I. Cocemasov, D.V. Crismari and A.A. Balandin, Appl. Phys. Lett., 102, 213109 (2013)
Alexander A. Balandin, University of California - Riverside12
Electron Mobility in Nanowires: Effect of the Electron Confinement
GaAs nanowire at T=200 K
Assumptions:confined electrons (infinite potential well)bulk phonons (acoustic and polar optical)ground state sub-band onlyionized impurity scattering
Conclusions: 1/ph increases with decreasing a
Results of J. Lee and M.O. Vassell, J. Phys. C: Solid State Physics, 17, 2525 (1984).
H. Sakaki, Jap J. Appl. Phys., 19, L735 (1980).
GaAs nanowire at low T
Assumptions:confined electrons (infinite potential well)remote ionized impurity scattering
Predictions: mobility increase > 106 cm2/Vs
Alexander A. Balandin, University of California - Riverside 13
Mobility Calculation in Silicon Nanowires: Bulk vs. Confined Phonons
c qw q
3/ 22ie
c V qr q r
q
qu
2, ( ) ( ) z
z
iq zq z z t z
dG dFq i q G r q F r e
dr drw r
u e e
( ) ( ) ( )1 0 2 0
( ) ( ) ( )3 0 4 0
( ) ( ) ( )
( ) ( ) ( )
n n n
n n nt t
G r C J q r C N q r
F r C J q r C N q r
22 2zq c qw
22 2t t zq c qw
Phonons in a cylindrical nanowire:
Bulk-like phonons:
21 2
ph
2( ) 1 ( ) ( )
z z z z z z
zz a k q k k q k
z
qk E N N
k
p w w
q q q q qq
u
Momentum relaxation rate due to phonons:
22 2
21 1imp 13
0
2( ) ln( )
2I
z zz
mN R Zek k R
k
pp
Momentum relaxation rate due to ionized impurities:
1/ 2 1/ 2000 0
2 ( ) ( )e f
d f dm
The low-field electron mobility in the nanowire:
fo() is the electron occupation number given by theFermi-Dirac distribution. In the non-degeneratecase, it is given by a Maxwellian distribution.
2/32/5*)(~ Tml2/312/1*)(~ TNm Ii
acoustic phonons
ionized impurities
Alexander A. Balandin, University of California - Riverside14
Evolution of Phonon Transport in Nanowires with “Acoustically Hard” Barriers
The size of the circles is proportional to the average divergence of displacement vector
Contribution of higher energy modes is negligible compared to the shown modes
“True” acoustic mode changes velocity from that in Si to the diamond
Contribution of the “true” acoustic mode to scattering decreases with increasing coating thickness
V.A. Fonoberov and A.A. Balandin, “Nano Letters, 6, 2442 (2006).
Alexander A. Balandin, University of California - Riverside 15
Phonon Engineering of Electron Mobility in Silicon Nanowires
At low T the mobility is limited by impurities and is proportional to T1/2, while at high T it is limited by phonons and is proportional to T-1/2
Electron mobility for diamond coated Si nanowire is between the limits corresponding to free-standing and clamped nanowire
A. A. Balandin and V. A. Fonoberov, "Nanometer-Scale Transistor Architecture Providing Enhanced Carrier Mobility," U.S. Patent 8,097,922
Alexander A. Balandin, University of California - Riverside
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Experimental Evidence of Phonon Confinement Effects in GaN Nanowires
Brillouin-light-scattering measurements and finite-element modeling of vibrational spectra in mono-crystalline GaN nanowires
W.L. Johnson et al., Nanotechnology, 23, 495709 (2012).
Alexander A. Balandin, University of California - Riverside
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Experimental Evidence of Phonon Confinement Effects in Nanostructures
“Thermal conductivities of the sub-20 nm diameter NWs are further suppressed by the phonon confinement effect beyond the diffusive boundary scattering limit.”
M.C. Wingert et al., Nano Lett., 11, 5507 (2011).
“We report the changes in dispersion relations ofhypersonic acoustic phonons in free-standing silicon membranes as thin as ∼8 nm. We observe a reduction of the phase and group velocities of the fundamental flexural mode by more than 1 order of magnitude compared to bulk values.”
J. Cuffer et al., Nano Lett., 12, 3569 (2012).
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Part II: Phonons in Graphene
IEEE Spectrum illustration of the discovery of unique thermal properties of graphene at UC Riverside (IEEE Spectrum, October, 2009)
The UCR Experiment
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Optical Phonons in Graphene: Raman Spectroscopy
Other techniques:
low-temperature transport study
cross-sectional TEM
few other costly methods
Visualization on Si/SiO2 substrates D band: A1g (~1350 cm-1); G peak: E2g; 2D band
A.C. Ferrari et al., Phys. Rev. Lett. 97, 187401 (2006).
I. Calizo, et al., Nano Lett., 7, 2645 (2007).
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Temperature Effects on Raman Spectrum –Converting Spectrometer into “Thermometer”
-150 -75 0 751576
1578
1580
1582
1584
1530 1575 16202500
5000
7500
10000
12500
G P
eak
Po
sitio
n (
cm-1)
Temperature (C)
G Peak Position Linear Fit of Data
Bi-Layer Graphene
slope = -0.015 cm-1/C
Raman Shift (cm-1)
Inte
nsity
(a
rb. u
nits
) Bi-layerGrapheneexc = 488 nm
G Peak1580 cm-1
Phonon frequency downshift with T is unusual when the bond-bond distances shorten with T since normallylattice contraction leads to the upward shift of the frequencies.
Temperature is controlled externally; very low excitation power on the sample surface is used (< 0.5 – 1 mW).
Optothermal technique for measuring thermal conductivity of graphene
Alexander A. Balandin, University of California - Riverside
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Raman Optothermal Measurement Procedure for Graphene
Laser acts as a heater: DPG
Raman “thermometer”: DTG=Dw/cG
Thermal conductivity: K=(L/2aGW)(DPG/DTG)
1( / 2 ) ( / ) .G G GK L a W Pc w D D
A.A. Balandin, et al., Nano Letters, 8, 902 (2008).
Bilayer graphene ribbon bridging 3-m trench in Si/SiO2 wafer
Connect DPD DPG through calibration
Alexander A. Balandin, University of California - Riverside
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Evolution of the Intrinsic Thermal Conductivity in Low-Dimensional Systems
S. Ghosh, W. Bao, D.L. Nika, S. Subrina, E.P. Pokatilov, C.N. Lau and A.A. Balandin, "Dimensional crossover of thermal transport in few-layer graphene," Nature Materials, 9, 555 (2010).
Experiment and Umklapp Scattering Theory Nonequilibrium Molecular Dynamics Study
Consistent with the prediction:
S. Berber,Y.-K. Kwon, and D. Tomanek, Phys. Rev. Lett., 84, 4613 (2000).
W.-R. Zhong et al., Appl. Phys. Lett., 98, 113107 (2011).
Simulations for graphene and FLG ribbons
Alexander A. Balandin, University of California - Riverside
Phonons in Isotopically Engineered Graphene
The thermal conductivity, K, of isotopically pure 12C(0.01% 13C) graphene was higher than 4000 W/mKat T~320 K and more than a factor of two higherthan in 50%-50% 12C and 13C graphene.2/1 Mw
13C and 12C difference: ~ 64 cm-1
S. Chen, Q. Wu, C. Mishra, J. Kang, H. Zhang, K. Cho, W. Cai, A.A.Balandin and R.S. Ruoff, "Thermal conductivity of isotopicallymodified graphene," Nature Materials, 11, 203 (2012).
Cooperation with Ruoff Group
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Klemens Model of Heat Conduction: Bulk Graphite vs. Graphene
2,max
, 2 2
1 ssU s
s B
M
k T
w w
P.G. Klemens, J. Wide Bandgap Materials, 7, 332 (2000).
Phonon Thermal Conductivity:
Umklapp life-time, which defines MFP:
2-D: C(w) ~ w K ~T-1w-1
3-D: C(w) ~ w2
wwww dCK jjjjp )()()( 2
N. Mounet et al, Phys. Rev. B 71, 205214 (2005).
Alexander A. Balandin, University of California - Riverside
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The Role of the Long-Wavelength Phonons in Heat Transport in Graphene
Graphene: 2,max
, 2 2
1 ssU s
s B
M
k T
w w
,max,min
ss ss
s B
M
k T L
w w
MFP = L – physical size of the system
Limitation on MFL: L= vs
Limiting low-bound frequency:
),/ln()/()2( 412Bmm ffTfK rp
2/123 4/ TLkfMf BmB p
Thermal conductivity in graphene:
Alexander A. Balandin, University of California - Riverside
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Divergence of the Lattice Thermal Conductivity in 2-D Crystal Lattices
K ~ log(N) in 2D
K ~ Nα in 1D, α≠1
N – system size[1] K. Saito, et al., Phys. Rev. Lett. 104, 040601 (2010).[2] A. Dhar. Advances in Physics 57, 457 (2008).[3] G. Basile et al. Eur. Phys. J. 151, 85 – 93 (2007).[4] L. Yang et al. Phys. Rev. E 74, 062101 (2006).[5] L. Delfini et al. Phys, Rev. E 73, 060201R (2006).[6] S. Lepri et al. Chaos 15, 015118 (2005).[7] J. Wang, B. Li. Phys. Rev. Lett. 92, 074302 (2004).[8] S. Lepri et al. Phys. Rep. 377, 1 (2003).[9] R. Livi and S. Lepri. Nature 421, 327 (2003).[10] O. Narayan et al., Phys. Rev. Lett., 89, 20601 (2002). [11] A. Dhar. Phys. Rev. Lett. 86, 5882 (2001).[12] A. Lepri and R. Livi, J. Stat. Phys. 100, 1147 (2000).[13] T. Pozen et al., Phys. Rev. Lett., 84, 2857 (2000).[14] S. Lepri et. al. Europhys. Lett. 43, 271 (1998).
Thermal conductivity in 2D lattice vs. Nx. Data is after S. Lepri et al. (Ref. [8]).
Consensus: The intrinsic thermal conductivity of 2-D or 1-D anharmonic crystals is anomalous.
Alexander A. Balandin, University of California - Riverside
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Uniqueness of Heat Conduction in GrapheneBreakdown of Fourier’s Law vs. Size-Dependent Intrinsic Thermal Conductivity
The phonon transport in graphene is 2D all the way down to zero frequency
D.L. Nika, S. Ghosh, E.P. Pokatilov, A.A. Balandin, Appl. Phys. Lett., 94, 203103 (2009).
,max,min
ss ss
s B
M
k T L
w w
Low-bound cut-off frequency is defined by the condition that the phonon MFP can not exceed the physical size of the graphene flake:
Alexander A. Balandin, University of California - Riverside
Engineering Phonons by Twisting Atomic Planes
Born-von Karman model for description of the carbon-carbon intra-layer interactions
Lennard-Jones potential for the inter-layer interactions
Phonons in Twisted Bilayer Graphene
A.I. Cocemasov, D.L. Nika and A.A. Balandin, “Phonons in twisted bilayer graphene” Phys. Rev. B, 88, 035428 (2013)],
Please see POSTER for details
Alexander A. Balandin, University of California - Riverside
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Part III: Phonons in van der Waals Materials
D. Teweldebrhan, V. Goyal, M. Rahman and A.A. Balandin, "Atomically-thin crystalline films and ribbons of bismuth telluride," Applied Physics Letters, 96, 053107 (2010). -Issue's Cover
Alexander A. Balandin, University of California - Riverside
Van der Waals Materials: Two-Dimensional Materials Beyond Graphene
D. Teweldebrhan, V. Goyal and A.A. Balandin, "Exfoliation and characterization of bismuth telluride atomic quintuplesand quasi-2D crystals," Nano Letters, 10, 1209 (2010).
Topological Insulators Benefits of Few-Quintuple Films Predicted High Thermoelectric
Figure of Merit
Alexander A. Balandin, University of California - Riverside
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A.A. Balandin and K.L. Wang, Phys. Rev. B (1998). A.A. Balandin and K.L. Wang, J. Appl. Phys. (1998).
The thermoelectric figure of merit: ZT=S2sT/(Ke+Kp)S is the Seebeck coefficient, s is the electrical conductivity and K is the thermal conductivity.
Electron Quantum Confinement Acoustic Phonon Confinement
M.S. Dresselhaus, et al. Phys. Solid State (1999).L.D. Hicks and M.S. Dresselhaus, Phys. Rev. B (1993).
Low potential barrier in Bi2Te3/Bi2Se3; Bi2Te3/Sb2Te3
Thermoelectric Motivation for Atomically Thin Films of Bi2Te3
Alexander A. Balandin, University of California - Riverside
Raman Spectroscopy of the Atomically Thin Films of Bi-Te Topological Insulators
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K.M.F. Shahil, M.Z. Hossain, D. Teweldebrhan and A.A. Balandin, "Crystal symmetry breaking in few-quintuple Bi2Te3 films: Applications in nanometrology of topological insulators," Appl. Phys. Lett., 96, 153103 (2010).
Alexander A. Balandin, University of California - Riverside
Room-Temperature Electrical Characterization Bi-Te Atomic Films
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Weak gating at RT
Resistivity is ~10-4 Wm
D. Teweldebrhan, V. Goyal, M. Rahman and A.A. Balandin, "Atomically-thin crystalline films and ribbons of bismuth telluride," Appl. Phys. Lett., 96, 053107 (2010).
Alexander A. Balandin, University of California - Riverside
Thermoelectric Energy Conversion with Stacks of Bi2Te3 Exfoliated Films
V. Goyal, D. Teweldebrhan and A.A. Balandin, “Mechanically exfoliated stacks of thin films of Bi2Te3
topological insulator films”, Appl. Phys. Lett. (2010).
ZT increase by ~140 – 250% at room temperature
The enhancement is expected to be larger at low T
Alexander A. Balandin, University of California - Riverside
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Charge Density Waves: Macroscopic Quantum State
CDW is a cooperative state of the ionic lattice and electron gas
1D and 2D metal-chalcogenides: NbSe2, NbSe3, TaS2, TiSe2
CDW can move in electric field
Progress in 1970 – 1980
Alexander A. Balandin, University of California - Riverside
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Phonon Spectrum Evolution with the TiSe2 Film Thickness
Main features are A1g peak at ~207 cm-1 and Eg peak at 233 cm-1
Peak at 316 cm-1 is more pronounced and appears near TC
Temperature at which the spectrum modification is observed is shifter to about ~225 K.
Intensity of the low-T Raman peaks varies from sample to sample
Emergence of the new Raman lines in TiSe2 is explained by formation of the CDW superlatticebelow the phase transition temperature
TiSe2
P. Goli, J. Khan, D. Wickramaratne, R.K. Lake and A.A. Balandin, Charge density waves in exfoliated films of van der Waals materials: Evolution of Raman spectrum in TiSe2, Nano Letters, 12, 5941 (2012).
Alexander A. Balandin, University of California - Riverside
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CDW Transition Temperature Scaling with Decreasing Thickness
CDW transition temperature vs. thickness of the exfoliated TiSe2 thin films.
temperature increases from ~200 K in the thick films (H~2 m) to ~240 K in the thin films (H~100 nm).
Major benefit for the proposed electronic applications
Recent theoretical work: M. Calandra, et al., PRB, 80, 241108 (2009)
TiSe2
P. Goli, J. Khan, D. Wickramaratne, R.K. Lake and A.A. Balandin, Charge density waves in exfoliated films of van der Waals materials: Evolution of Raman spectrum in TiSe2, Nano Letters, 12, 5941 (2012).
Alexander A. Balandin, University of California - Riverside
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Collective Current Regime in TaSe2Channel Devices
Increase in the apparent threshold voltage is owing to (i) High
concentration of defects
(ii) Size effects(iii) Possible
voltage drop on electrodes
(iv) Channel non-linearity
Alexander A. Balandin, University of California - Riverside
The switch to multi-core designs alleviates the growth in the thermal design power (TDP) increase but does not solve the hot-spot problem
Non-uniform power densities leading to hot-spots (>500 W/cm2)
Data is after R. Mahajan et al., Proceed. IEEE (2006)
IEEE Spectrum illustration of the thermal issues in the feature article Chill Out: New Materials and Designs Can Keep Chips Cool by A.A. Balandin.
No BIG fan solutions!
Part IV: Practical Applications of Phononics
Alexander A. Balandin, University of California - Riverside
Increasing Importance of the Thermal Interface Materials - TIMs
TIMs are materials with the relatively high thermal conductivity introduced to the joint to fill the air gaps.
Current TIM based on polymer, grease filled with silver, alumina require 50-70% loading to achieve 1-5 W/mk.
Conventional TIMs: K=1-5 W/mK at the volume fractions f of filler ~50% at RT
Companies need K=25-30 W/mK
Alexander A. Balandin, University of California - Riverside
Graphene Enhanced Thermal Interface Materials
aqueous solution of sodium cholate
K.M.F. Shahil and A.A. Balandin, "Graphene - multilayer graphene nanocomposites as highly efficient thermal interface materials," Nano Letters, 12, 861 (2012).
Alexander A. Balandin, University of California - Riverside
Graphene TIMs with Strongly Enhanced Thermal Conductivity
Record-high enhancement of K by 2300 % in the graphene-polymer at the loading fraction f =10 vol.%.
K of the commercial thermal grease was increased to K=14 W/mK at the small loading f=2 vol. %
K.M.F. Shahil and A.A. Balandin, "Graphene -multilayer graphene nanocomposites as highly efficient thermal interface materials," Nano Letters, 12, 861 (2012).
Alexander A. Balandin, University of California - Riverside
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Can Graphene Make PCM Not Only to Store Heat but also to Conduct it Away?
P. Goli, et al., "Graphene-Enhanced Hybrid Phase Change Materials for Thermal Management of Li-Ion Batteries" (2013) –available on arXiv
Alexander A. Balandin, University of California - Riverside
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Hydrocarbon – Graphene Composites as PCMs with Enhanced Thermal Conductivity
P. Goli, et al., "Graphene-Enhanced Hybrid Phase Change Materials for Thermal Management of Li-Ion Batteries,“ (2013) – available on arXiv.
The thermal conductivity enhancement factor, h=(K-Km)/Km, of about 60 at the 1 wt. % loading fraction is exceptionally high
It is unlikely that uniformly dispersed graphene flakes with a lateral size in the range from 150 to 3000 nm form a thermally percolating network at 1 wt. %
Strongly increased thermal conductivity of the composite is explained by good attachment of hydrocarbon molecules to graphene flakes
Alexander A. Balandin, University of California - Riverside
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Testing CnH2n+2 – Graphene Composites for PCM for Battery Thermal Management
Reduced temperature rise and increased reliability of Li-ion batteries
Alexander A. Balandin, University of California - Riverside
Graphene Quilts for Thermal Management GaN Technology
Z. Yan, G. Liu, J.M. Khan and A.A. Balandin, Graphene-Graphite Quilts for ThermalManagement of High-Power Transistors, Nature Communications (2012).
GaN HFETs were used as examples of high-power density transistors; PMMA was utilized as thesupporting membrane for graphene transfer to a desired location; the alignment was achieved withthe help of a micromanipulator
Alexander A. Balandin, University of California - Riverside
Reduction of the Hot-Spot Temperature
The hot-spots temperature near drain contacts can be lowered by as much as ~ 20oC in such devicesoperating at ~13-W/mm – translates to an order of magnitude improvement in MTTF
Alexander A. Balandin, University of California - Riverside
Graphene-on-Diamond –Carbon-on-Carbon Technology
Typical graphene FETs on SiO2/Si reveal JBR on the order of 108 A/cm2, which is ~100× larger than the limit for the metals but still smaller than the maximum achieved in CNTs
Alexander A. Balandin, University of California - Riverside
Graphene Interconnects with Extraordinary High Breakdown Current Density
J. Yu, G. Liu, A. Sumant and A.A. Balandin, Graphene-on-diamond devices with increased current-carrying capacity:Carbon sp2-on-sp3 technology, Nano Letters, 12, 1603 (2012).
Alexander A. Balandin, University of California - Riverside
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Basics of CDW Logic Gates
Schematic view of the CDW-based EX-NOR gate. Input data is encoded into the phase of the CDW (e.g. f= 0 corresponds to logic 0, and f = p corresponds to logic 1). The amplitude of the applied voltage is just below the threshold (e.g. Vin = 8 mV; Vth = 9 mV). The constructive interference produces CDW of the double amplitude sufficient for de-pinning, which opens the channel. There is no electric current flow in the case of destructive interference.
Alexander A. Balandin, University of California - Riverside
Practical Motivations for Collective State as Computational State Variables
Power dissipation became the limiting factor to the continued scaling of size and speed of the CMOS transistors
If N electrons are in a collective state then the minimum dissipation limit for one switching cycle can be reduced from NkBTln(2) to kBTln(2)
Charge density waves (CDW) are collective states, which can exist on a macroscopic scale near room temperature
CDW can be utilized for Boolean and non-Boolean logic gates and information processing similar to spin waves
Unconventional materials require innovative techniques for material synthesis and device fabrication
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Alexander A. Balandin, University of California - Riverside
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RT Thermal Conductivity of Carbon Materials:
Diamond: 1000 – 2200 W/mK
Graphite: 20 – 2000 W/mK
DLC: 0.1 – 10 W/mK
a-C: 0.01 – 1 W/mK
NCD-MCD: 1 – 1000 W/mK
CNTs: 1000 – 3500 W/mK
Graphene: 2000 – 5000 W/mK
Take Home Message: Thermal Properties of Carbon Materials
Alexander A. Balandin, University of California - Riverside
Outlook for Phonon Engineering
Phonon confinement effects in nanostructures are observed at room temperature
Nanometer scale is essential for observing and utilizing the phonon confinement effects
Technology has reached the state required for engineering phonon modes
Strong practical motivation due to the problems of heat removal from downscaled computer architectures
Phonon engineering combined with electron band-structure engineering can bring previously unattainable functionality
Graphene and van der Waals materials offer new opportunities for phonon engineering 53
Alexander A. Balandin, University of California - Riverside
Acknowledgements
Nano-Device Laboratory (NDL), UC Riverside, 2010 – 2013